• East Asian mathematical journal
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• v.36 no.1
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• pp.25-34
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• 2020

The classical limit theorems like strong law of large numbers, central limit theorems and law of iterated logarithms are fundamental theories in probability and statistics. These limit theorems are proved under additivity of probabilities and expectations. In this paper, we investigate strong law of large numbers under sub-linear expectation which generalize the classical ones. We give strong law of large numbers under sub-linear expectation with respect to the partial sums and some conditions similar to Petrov's. It is an extension of the classical Chung type strong law of large numbers of Jardas et al.'s result. As an application, we obtain Chung's strong law of large number and Marcinkiewicz's strong law of large number for independent and identically distributed random variables under the sub-linear expectation. Here the sub-linear expectation and its related capacity are not additive.

• Bulletin of the Korean Chemical Society
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• v.35 no.3
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• pp.815-820
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• 2014

We applied the two-color resonant two-photon ionization and mass-analyzed threshold ionization techniques to record the vibronic and cation spectra of 2,4-difluorophenol. As supported by our theoretical calculations, only the cis form of 2,4-difluorophenol involves in the two-photon photoexcitation and pulsed field ionization processes. The band origin of the $S_1{\leftarrow}S_0$ electronic transition of cis-2,4-difluorophenol appears at 35 647 ${\pm}2cm^{-1}$ and the adiabatic ionization energy is determined to be 70 $030{\pm}5cm^{-1}$, respectively. Most of the observed active vibrations in the electronically excited $S_1$ and cationic ground $D_0$ states mainly involve in-plane ring deformation vibrations. Comparing these data of cis-2,4-difluorophenol with those of phenol, cis-2-fluorophenol, and 4-fluorophenol, we found that there is an additivity rule associated with the energy shift resulting from the additional fluorine substitution.

• The Mathematical Education
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• v.45 no.3 s.114
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• pp.367-373
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• 2006

This study suggests that it is necessary to prove that the values of three areas of a triangle, which are obtained by the multiplication of the respective base and its corresponding height, are the same. It also seeks to deeply understand the meaning of Area formula of triangles by exploring some questions raised in the analysis of the proof. Area formula of triangles expresses the invariance of congruence and additivity on one hand, and the uniqueness of parallel line, one of the characteristics of Euclidean geometry, on the other. This discussion can be applied to introducing and developing exploratory learning on area in that it revisits the ordinary thinking on area.

• Journal of the Korean Chemical Society
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• v.6 no.2
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• pp.170-175
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• 1962

The ultraviolet and visable absorption spectra of trans, cis-azoxybenzene, substituted azoxybenzenes and their conjugate acids have been studied. The 320-350$m{\mu}$ main bands of free-base of azoxybenzenes are due to ${\pi}{\to}{\pi}^{\ast}$ transition. These bands of their conjugate acids shown bathochromic shift into visible range. The following emperical relationship between absorption maxima of the main bands was found. ${\lambda}_{max}={\lambda}^{\circ}_{max}+{\Delta}{\lambda}_x+{\Delta}{\lambda}_y$ This relationship in terms of wave number is also hold in good agreement. ${\nu}={\nu}_{\circ}-({\Delta}{\nu}_x+{\Delta}{\nu}_y)$

• Journal of the Korea Safety Management & Science
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• v.11 no.2
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• pp.117-126
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• 2009

We develop methods for propagating and analyzing EPCI(Extended Process Capability Index) by using the error type that classifies into accuracy and precision. EPCI developed in this study can be applied to the three combined processes that consist of production, measurement and calibration. Little calibration work discusses while a great deal has been studied about SPC(Statistical Process Contol) and MSA(Measurement System Analysis). EPCI can be decomposed into three indexes such as PPCI(Production Process Capability Index), PPPI(Production Process Performance Index), MPCI(Measurement PCD, and CPCI(Calibration PCI). These indexs based on the type of error classification can be used with various statistical techniques and principles such as SPC control charts, ANOVA(Analysis of Variance), MSA Gage R&R, Additivity-of-Variance, and RSSM(Root Sum of Square Method). As the method proposed is simple, any engineer in charge of SPC. MSA and calibration can use efficientily in industries. Numerical examples are presentsed. We recommed that the indexes can be used in conjunction with evaluation criteria.

• Korean Journal of Pharmacognosy
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• v.8 no.1
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• pp.17-21
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• 1977

$^{13}C-NMR$ behaviors of phenolic compounds such as phenol, catechol, pyrogallol, resorcine, phoroglucine and hydroquinone were studied. From the study on the effects of OH-substitution on benzene and its dervatives it was found that the additivity rule can be applied to the ortho-and para-effect but not to the meta-effect for the OH-function. The empirically calculated chemical shifts regarding the o-and p-effects coincide very well with the results of measurement. The chemical shifts of the phenolic compounds can be classified into three types. 1) Catechol-type C-1 and C-2 145 ppm C-3 and C-6 116-107 ppm 2) Pyrogallol-type C-1 132ppm C-2 and C-6 146ppm C-3 and C-5 106ppm 3) Resorcin-type C-1 and C-3 159ppm C-2 103-95ppm C-4 and C-6 107ppm

• Journal of the Korean institute of surface engineering
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• v.47 no.1
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• pp.48-52
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• 2014

Electric conductivities of $LaCl_3$-KCl binary melts have been measured by the Kohlausch bridge method over the range from their liquidus temperatures to about 1280 K. The electric conductivity increased with the content of KCl for all over the composition range of binary melts. The composition dependence of the electric conductivity and molar conductivity for the binary melt showed a non-linear relation from the additivity line, and the deviation showed a maximum value at about 60 mol.% KCl. The deviation implies the existence of complex ion of $LaCl^{4-}$ in the melt. Activation energy for electric conductivity of the binary melts decreased monotonously with increasing content of KCl.

• Journal of Welding and Joining
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• v.18 no.5
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• pp.55-62
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• 2000

A metallurgical model for the phase transformation kinetics at Coarsened Grain Heat Affected Zone(CGHAZ) on the basis of Johnson-Mehl-Avrami equation(JMA equation) was proposed. In this model, the effect of prior austenite grain size on the transformation and the morphological changes of ferrite were considered. Isothermal dilatometer tests were performed to determine the effect of prior austenite grain size (AGS) on the austenite decomposition to ferrite and pearlite in a plain carbon steel. By comparing the calculated volume fraction with measured data, the reliability of the developed model was discussed.

• Journal of the Korean institute of surface engineering
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• v.39 no.6
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• pp.282-287
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• 2006

Viscosities of $LaCl_3-NaCl$ binary melts were measured by the capillary method over the range of their liquidus temperatures to about 1200K. The cell constant were determined by using pure water. The results obtained are summerized as follows: Viscosities were decreased with the content of NaCl for all over the composition range of binary melts. Composition - viscosity relation for the binary melts show a non-linear from the additivity line and the deviations shows a maximum at about 60 mol% NaCl. This suggests the existence of the complex ion of $LaCl_4^-$ in the melt. Activation energy for viscous flow of the binary melts decrease monotonously with the increasing content of NaCl.

• Journal of the Ergonomics Society of Korea
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• v.3 no.1
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• pp.19-24
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• 1984

As in dynamic muscular activity, to support one's body may be regarded as the static workload. An examination is made of the relationship between heart rate and oxygen uptake of three male graduate students in static working postures (sitting, squatting and standing). Though it has been believed that there exists a linear relationship between heart rate and oxygen uptake, this thesis shows that both have no relationship in the case of static postures, and that they may depend upon the characteristics of postures rather than the static workload. These results are discussed analytically. The additivity between static body postures and holding up one's hands at his maximum height is tested. Compared with the sum of energy expenditure in balancing one's body and holding up hands, the net rate of energy expenditure in performing them simultaneously is equivalent. In the case of static postures, the importance of the awareness of the characteristics and relevance of the measures is discussed.